Problem: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2}{x + 10} = \dfrac{100}{x + 10}$
Multiply both sides by $x + 10$ $ \dfrac{x^2}{x + 10} (x + 10) = \dfrac{100}{x + 10} (x + 10)$ $ x^2 = 100$ Subtract $100$ from both sides: $ x^2 - (100) = 100 - (100)$ $ x^2 - 100 = 0$ Factor the expression: $ (x + 10)(x - 10) = 0$ Therefore $x = -10$ or $x = 10$ However, the original expression is undefined when $x = -10$. Therefore, the only solution is $x = 10$.